Research Of Stability For Several Classes Of Common Ecological Models

In this paper, we consider several classes of common ecological models such as predator prey model and epidemic model, and obtain uniform persistence and stability of the solution or the periodic solution by constructing appropriate Lyapunov functional and using eigenvalue analysis to model's linear similar system at the equilibrium.In chapter 2, we deal with a non-autonomous periodic competitive Lotka-Volterra model with distributive delay and a Lotka-Volterra model with distributive time delay and Rolling type II functional response, and get the asymptotic quality of models by means of using Lyapunov functional method. Both of them have discrete diffusion.In chapter 3, two nonlinear modified Gilpin-Ayala models with distributive delay and continuous diffusion are studied. Some simple sufficient conditions for globally asymptotically stable and asymptotically stable of the unique positive equilibrium point are established by constructing Lyapunov functional.In chapter 4, a SIRS epidemic model with stage-structure consisting immature and mature stage and time delay is studied. By using eigenvalue analysis we obtain that the asymptotic behavior of the model and the local asymptotic stability of its equilibrium.